Document Type: Research Paper
University of Tehran, College of Engineering, Department of Engineering Science
Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined to be min(| S | +m(G − S)) where S ⊂ V (G) and m(G − S) is the maximum order of the components of G − S. Similarly the edge-integrity of G is I′(G) := min(| S | +m(G − S)) where now S ⊆ E(G). Here and through the remaining sections, by an I-set (with respect to some prescribed graph G) we will mean a set S ⊂ V (G) for which I(G) =| S | +m(G − S). We define an I′-set similarly.
In this paper we show a lower bound on the edgeintegrity of graphs and present an algorithm for its computation.